This is a simple concept and sort of hard to pull off. You knock the wiggler over by blowing up a plant when it's near the plant. So watch where the wiggler is going and water the plant it's about to go around, to knock it over. Then leap on its belly and stomp-pound the one with the arrow over it. You have to do this a few times to get him completely dead, but then the shine is right on the beach so that part is easy.
Super Mario Sunshine Walkthrough